The Age Puzzle
Five years ago, Maria was three times as old as her son. In five years, she will be twice as old as her son. How old are Maria and her son now?
A box of biscuits
A box of biscuits contains 36 biscuits. 20 biscuits have foil wrappers. 15 are chocolate biscuits with foil wrappers. If 9 are not chocolate and do not have a foil wrapper, then how many chocolate biscuits are there?
Define Variables:
ReplyDeleteLet Maria's current age be M and her son's current age be S.
Translate the First Condition:
Five years ago, Maria was three times as old as her son.
M−5=3(S−5)
Translate the Second Condition:
In five years, she will be twice as old as her son.
M+5=2(S+5)
Set Up the Equations:
Now we have two equations:
M−5=3S−15
M+5=2S+10
Simplify the Equations:
Simplifying both equations:
M=3S−10
M=2S+5
Solve the Equations:
Since both expressions equal M, set them equal to each other and solve for S:
3S−10=2S+5
S=15 (Maria's son is 15 years old)
Find Maria's Age:
Substitute
S=15 into either equation to find M
M=3(15)−10=45−10=35 (Maria is 35 years old)
So, Maria is currently 35 years old, and her son is 15 years old.